Re: Explanation of K

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

I wrote: 

> For a typical TC, the higher modes are less than 5% of the
> fundamental amplitude.  Increasing the coupling raises this
> fraction.

Antonio wrote:

> ...I would like to see a study about how are these waves in
> function of the coupling coefficient, to verify if they
> really are significantly larger when the coupling coefficient
> is high. 
 
> ...but would the relative amplitudes of the modes be much
> different for different coupling coefficients?

> Where is this result shown in your investigation 

Antonio, I'm afraid that you've exposed a hole in my argument -
I've not presented any evidence to support this claim.

I have base current data from Terry's lab for different k
factors, and they do suggest that the mode content increases
with k, at least up to a point anyway.  For example, consider
the setup shown in

 http://www.abelian.demon.co.uk/tssp/tfss310501/P5310006.JPG

in which Terry's SS gap can impulse the secondary either through
the flat primary (k circa 0.2) or the helical (k circa 0.35).

The base waveform and spectrum for the low-k primary are in

 http://www.abelian.demon.co.uk/tssp/tfss270501/

in which the mode 3 amplitude is about 10% that of the
two fundamentals. 

The high-k base current waveform is in 

 http://www.abelian.demon.co.uk/tssp/tfss310501/Tek00002.gif

which has the spectrum

 http://www.abelian.demon.co.uk/tssp/tfss310501/tek00001.ft.gif

Mode 3 is now at around 40% and is very visible in the time
domain also.  The volts/turn in the lower third of this
secondary will therefore (occasionally) be around double
that of the low-k arrangement, for the same bang size.

I'm afraid that's all we've got to go with.  I've not done a more
thorough quantitative comparison yet, because the model I'm using
struggles a bit at high-k:  the close proximity of the high-k
primary makes it hard to calculate the distributed capacitance
with enough accuracy to pin down the mode frequencies sufficiently
well to compare amplitudes and phases.  I'm working on that.

I do agree, this does really call for a decent experiment to settle
the matter once and for all.  Come to think of it, might make a nice
science fair project (Hi CJ, are you still following this thread?).

> dv/dt and di/dt peaks are not much affected (they are proportional
> to the secondary current and voltage, and these are limited by
> energy conservation).

Ok on the (almost) invariant peak dv/dt in the lumped model, I
fully agree.  Just that this is one of the few cases where the
lumped model misses out on a potentially important piece of
physics.

> Would the peak of dv/dx increase significantly with k?

I think so, but I can't say for sure.  I'm just pointing out the
possibility.  More work is needed.

For those interested - some background on why these higher
modes are excited:

See the mode plot for Terry's low-k setup with the flat primary.

 http://www.abelian.demon.co.uk/tssp/tfss310501/tfsm2-p.modes.gif

Notice the similarity of the current profiles of the two lowest 
modes, at 219.3kHz and 273.3kHz, the two which, with almost equal
amplitude, make up the familiar beat envelope.  These two modes
have opposite phase of primary voltage.  If they had indentical
shape, then an equal and opposite amplitude of each mode would
exactly cancel all the secondary current to zero and leave the
system in the correct starting state - ie a primary charge and
zero current everywhere.  It is the slight imbalance between the
two current profiles which demands some excitation of the other
available modes in order to make the initial secondary current
add up to zero all along the coil.

The shape of these two modes diverges further when k is increased,
The lowest three modes predicted for Terry's high-k test,
are shown in 

 http://www.abelian.demon.co.uk/tssp/tfss310501/tfsm3-p.modes.gif

Note how the shape of the lowest two modes has diverged,
particularly in the region of the secondary covered by the
cylindrical primary.  You can see that it needs more than a whiff
of mode 3 to fill that gap - about 4 times as much compared with
the low-k.

Just to make this clear, we have to match the starting condition of
the secondary, which is zero current everywhere.  We start out with,
say, equal amounts of the lowest two modes, and subtract say the 
green from the red.  This cancels nicely to zero at 33% height,
but we have a residue elsewhere, which we try to get rid of by
invoking a little mode 3 (blue).  Choosing the mode 3 amplitude and
fiddling slightly with the first two modes to get the best possible
fit, still leaves a residue, so we bring in mode 4, and so on. 
No it doesn't matter what order we apply the modes - mathematicians
would say they are orthogonal,  and that also means that there is one
unique choice of mode amplitudes and phases which matches our starting
conditions, and is thus set into motion the moment the gap fires. 
If we could hear the thing ringing, this set of mode amplitudes would
describe its tone.

I'm not sure, but I think that two different primaries made to fit
the one secondary, and engineered to have indentical k, could give
different amounts of mode 3, if one primary had a more even
distribution of coupling than the other.  That's just a conjecture.

Incidentally, there is an mpeg movie of this high-k secondary at 
 http://www.abelian.demon.co.uk/tssp/tfsm3-p-k=0.35.mpeg
(1.4Mbyte, 22 seconds)
which shows the voltage profile along the secondary, and another
showing the voltage *gradient*,
 http://www.abelian.demon.co.uk/tssp/tfsm3-pdv-k=0.35.mpeg
(1.8Mbyte, 22 seconds)

Terry may have a mirror copy of these on hot-streamer-dot-com

Sorry for the long post, and forgive me for hijacking this thread
in order to draw attention to a topic that could do with a bit more
discussion and experiment.
--
Paul Nicholson
Manchester, UK
--